Details

sample254.0ms

Algorithm

intervals

Results

180.0ms	156×	body	1280	valid
44.0ms	64×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	42	18
done	42	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.5b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

11.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series173.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

86 → 86

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	196	1763
1	391	1589
2	1170	1307
3	4765	1227
done	5000	1215

prune500.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

18.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
46.0ms	(* (sin lambda1) (sin lambda2))
57.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify678.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	177	2086
1	473	1975
2	1957	1726
done	5001	1726

prune548.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
0.4b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
25.9b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
2.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series183.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
67.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
46.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify2.3s

Counts

87 → 87

Iterations

Useful iterations: 3 (451.0ms)

Iter	Nodes	Cost
0	139	1760
1	308	1482
2	992	1310
3	4184	1309
done	5000	1309

prune520.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))) R)
0.3b	(log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
0.3b	(expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))
0.7b	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`acos-asin` `log1p-udef` `expm1-log1p` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

3.0ms	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))) R)
0.0ms	(log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
0.0ms	(expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))
0.0ms	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))) R)
263.0ms	(log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
268.0ms	(expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))
15.0ms	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))

simplify929.0ms

Counts

64 → 64

Iterations

Useful iterations: 3 (236.0ms)

Iter	Nodes	Cost
0	111	1740
1	214	1611
2	609	1404
3	2162	1397
done	5000	1397

prune360.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.1b

regimes532.0ms

Accuracy

0% (0.3b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	30	28
done	30	28

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4828×	body	1280	valid
1.4s	2038×	body	640	valid
318.0ms	708×	body	320	valid
87.0ms	291×	body	160	valid
21.0ms	130×	body	80	valid
20.0ms	6×	body	2560	valid